Black Holes Essay, Research Paper
Stars can turn into varieties of things as they collapse, including white dwarfs, neutron stars, and black holes. A black hole is suggested to be the end product of a large star that is collapsing into itself, due to the fact that gravitational acceleration is calculated by the formula;
Where mb is the mass of the black hole, as the radius, r, of the star decreases, the gravitational field on its surface increases. This causes a chain reaction in which a greater force is put on the star to collapse, thus decrease in size even further, and the gravity of its surface increases. It is suggested that a star would have to have a mass equivalent to three times that of our Sun to become a black hole. If though a star with an equivalent mass to the Earth were to collapse into a black hole, the space that all of the matter would take up would have a radius of less than 9mm. It is easy to see that the density of this would be huge-thus demonstrating why it would have such notable effects. The gravitational field created would have important effects to its surrounding environment, producing signs for astronomers to observe when looking for a black hole.
Einstein s theory of general relativity suggests that close to the star itself, strong distortions occur in the structure of space. He found that the acceleration was equal when caused by changing motion, compared to when changed by gravitational fields. From this, we deduce that at the point of a gravitational field, space is actually curved such that moving particles follow the same path as they would if they were being accelerated. This has applications toward photons of light as well as any other particle.
The effects of this gravitational field produces an enhancement of the curvature of space, in terms of a photon of light projected from the surface of the star that is not directly along the path of the normal. It becomes deflected, causing an increased angle compared to the angle that it was projected at. Similarly, light that grazes the surface of a strong gravitational sphere is deflected in the same way. The stronger the gravitational field is, the greater angle of deflection and the greater the velocity of the wave that has to be projected to escape the field. As the density increases, the field s pull is so great that the photon of the light is directed horizontally at the field and deflected into the orbit of the star.
The star s light may be projected from the surface of the star to escape its gravitational field. When the projection s angle is equal to that of the normal, the light is projected away at any other angle than that of the normal. The stronger the gravitational field, the greater the deflection, and the smaller the angle becomes that the light is allowed to project away from the surface without being pulled into orbit. Thus as the star becomes more dense, its gravitational field s strength increased, until eventually the angle at which light is allowed to project away from the star is zero degrees. As light has the greatest velocity of anything known, and is said to go at the natural speed limit, as soon as light cannot escape from the boundary of the decaying star, neither can anything else. At this point, light from both the star and that hitting the field from the other sources cannot escape, thus a black hole is born.
Black holes were first understood by Kurt Schwarzchild well over 60 years ago. He proposed the properties that he expected the outer limit of the black hole to exhibit. He gave his name to the radius at which a star has a strong enough gravitational field to trap photons of light. This Schwarzchild radius, as is became known, was only dependant on the mass of the star in question, and was proportional to it. For instance, if a star had a mass of five times that of our Sun, its Schwarzchild radius would be 15km. As soon as the collapsing star has shrunk beyond its Schwarzchild radius it is said to have passed its event horizon as no outside observations can be made into it. The photon-sphere however is the point when light is forced to orbit the star, but is not pulled into the event horizon.
The point at which the star s mass is centered is called singularity. This, in his equation, lay at the very center of the black hole, and is considered to center of its gravitational field. The singularity is infinitesimally small because mathematically it is found to be a single point.
As all stars are known to rotate, it is almost impossible that we would be able to find an example of the Schwarzchild black hole in nature. An Australian mathematician named Roy P. Kerr only discovered the relative equations to this fact in 1963. He found them accidentally while working on an other problem, and found that although the spinning black hole held resemblances to the Schwarzchild model, there were also distinct differences. In this new type of black hole, a body that enters it would be forced to move in a spinning motion down towards the singularity like water in a plughole. The limit at which light can still escape this dragging force is known as stationary limit. The momentum of the spin decreases the size of the event horizon, the limit between this and the stationary limit being the ergosphere. On a theoretical level, a body traveling faster than the speed of light within the ergosphere could escape it, yet there is no escape from being dragged around within it. The ergosphere is thought to produce an oval shape, being in contact with the poles of the event horizon, while on the equator having double the diameter of the event horizon.
It is mathematically possible that the speed of the spin of a black hole could cause the shrinking of the event horizon such that it disappears and the singularity is left on view. This would cause a naked singularity. This would not display the usual gravitational traits of a black hole and would be possible to blunder into without any previous warning. It also carries the implication that we could potentially travel freely in and out of singularity, as the event horizon is no longer present. If this were the case, by going into the orbit of a naked singularity, time travel into the past could occur. In general, this is conceived to be an impossible situation, as black hole properties are assumed by the size of the mass alone, with the charge and spin having little effect.
These Kerr black holes would have a singularity that takes form of a ring. It s singularity is not space-like as demonstrated in the other model, but time-like instead. Only objects that enter the event horizon on its equator would be subject to destruction via the singularity. The interior of the singularity is an area of negative space-time, implying the reversal of the force of gravity at this point. Another possible concept is that of objects within this plain having a negative radius, but no one has yet been able to fathom this idea rationally.
It has also been suggested that other black holes were created when the Big Bang occurred. These black holes were tiny, some as little as .0000001kg. We know that the density of matter as it crosses the event horizon varies inversely to the mass of the black hole such that the black holes of this miniscule nature must have had enormous pressures applied to create them. These pressures were only thought to exist during the creation of the universe, as we know it. There is no evidence of their existence except for in the laws of quantum mechanics. It has been put forward by Hawking that these black holes could have evaporated.
It is known that the components of particles can be split to particles and antiparticles. When this occurs and the pair re-meet, they annihilate each other, and energy is created. Similarly, energy can be converted into pairs of particles. This is known as pair production, and only works because mass and energy are equivalent. Taking this idea further, matter can be created from for very brief periods of time. As it occurs almost simultaneously, it does not violate the conversation laws. If this occurred near to a black hole, and half of the pair was to fall into it, the inevitable annihilation could not occur. The other half of the pair would be able to escape. Energy is created. This energy has to have a notable source, as energy cannot be created or lost. The source of such energy is the black hole itself. As it is robbed of energy, it is also robbed of its equivalent mass, thus the black hole evaporates due to pair production. This event would only have a noticeable consequence on the smallest of the black holes. If this process did occur, we would expect to see occasional bursts of gamma radiation being emitted from these mini black holes.
As we obviously cannot see black holes, the only thing we can do to ascertain their existence is applying theoretical knowledge and observe the things that we suspect they cause. Detection of black holes is most likely to occur when we find an invisible object that has a mass, which could only possibly demonstrate one. Even then, we are working on the assumption that white dwarfs and neutron stars are unable to survive at such a mass. One way of calculating the mass of an object we cannot see is to follow the orbit around of a companion star. If this star is found to be part of a binary system, with an invisible partner, then the mass of the companion can be calculated via spectral and visual analysis. If this mass is found to be in excess of 3 solar masses, then a black hole is presumed to have been found. Another way is by examining the matter that they pull toward themselves. This matter forms an accretion disk, which due to forces acting upon it, become hot enough to emit x-rays. These in turn can be detected and provide us with information on the fields acting upon them.
A black hole is said to encompass the four dimensions of space and time, thus as a body approaches the event horizon, time is distorted due to the force of acceleration, and force of the field. To an outside observer, it would slow gradually, and along with it, the wavelengths, although maintaining velocity is shifted. As the body becomes even closer to the event horizon, time appears to stop. Strong tidal forces would cause the body to be ripped apart. Upon reaching the event horizon, the body would never be seen again, and is thought by scientists to race irreversibly towards the singularity, and become infinitely more dense.
Although black holes have never been seen as such, their effect on the surroundings is clear. Thus by a principle called Occam s Razor, the explanation of any phenomenon that requires the fewest arbitrary assumptions is the most likely to be the correct one. We assume that black holes exist, and continue to make their own individual mark in the universe we live in.
A Brief History of Time: From the Big Bang to Black Holes by Stephen W. Hawking
Black Holes and Neutron Stars by Christopher Miller
The Dynamic Universe by Theodore P. Snow
Exploration of the Universe by Abell, Morrison, and Wolf
Searching for Dark Matter by Mario Mateo